Question: Solve for $x$ and $y$ using elimination. ${-5x+2y = -26}$ ${-2x+y = -9}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-2$ ${-5x+2y = -26}$ $4x-2y = 18$ Add the top and bottom equations together. $-x = -8$ $\dfrac{-x}{{-1}} = \dfrac{-8}{{-1}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {-5x+2y = -26}\thinspace$ to find $y$ ${-5}{(8)}{ + 2y = -26}$ $-40+2y = -26$ $-40{+40} + 2y = -26{+40}$ $2y = 14$ $\dfrac{2y}{{2}} = \dfrac{14}{{2}}$ ${y = 7}$ You can also plug ${x = 8}$ into $\thinspace {-2x+y = -9}\thinspace$ and get the same answer for $y$ : ${-2}{(8)}{ + y = -9}$ ${y = 7}$